Humble Pi: When Math Goes Wrong in the Real World

by Matt Parker

Unlikely events can happen. On June 7, 2016, Colombia was playing Paraguay in the 2016 Copa América. The referee flipped a coin to see which soccer team got to choose which end of the field their goal would be. Except the coin landed perfectly on its edge. After only a moment’s hesitation, and a few laughs from the nearby players who saw it happen, the referee picked the coin up and managed to flip it successfully. I will accept that falling into grass makes an edge landing more probable. A coin landing on its edge on a hard surface is almost impossible. I believe the coin with the highest chance of landing on its edge is the UK old-style £1 coin (in circulation from 1983 to 2017), which is the thickest coin I’ve seen in daily use. To check how likely it is to land on its edge, I sat down and spent three days flipping one. After ten thousand flips, it had landed on its edge fourteen times. Not bad. I suspect the new £1 coin will have similar odds, but I’ll leave those ten thousand flips to someone else. For something like the much thinner US nickel, I suspect it would take tens of thousands of flips for even a single edge case. But it is still possible. If you want something unlikely to occur, you simply need the patience to create enough opportunities to allow it to happen. Or, in my case, patience, a coin, a lot of free time, and the kind of obsessive personality that keeps you sitting in a room flipping a coin by yourself, despite the desperate pleas of your friends and...